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There are six different models that are to appear in a fashion show.

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There are six different models that are to appear in a fashion show.  [#permalink]

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New post 25 Jun 2015, 03:36
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There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?

A. 72
B. 48
C. 64
D. 24
E. 8

Source: Platinum GMAT
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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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New post 25 Jun 2015, 04:13
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Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?

A. 72
B. 48
C. 64
D. 24
E. 8

Source: Platinum GMAT
Kudos for a correct solution.


Since we have 3 continental pairs (EU, SA, NA), these 3 pairs have 3*2*1 = 6 Combinations. Within each pair, you have however 2 different ways to put them together for each of the pair (2*2*2 = 8). So we have 6*8 = 48.

Please correct me if im wrong.

Answer B.
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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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New post 25 Jun 2015, 05:28
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Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?

A. 72
B. 48
C. 64
D. 24
E. 8

Source: Platinum GMAT
Kudos for a correct solution.


Let's say that Models of Europe are represented by E1 and E2 respectively

Let's say that Models of South America are represented by S1 and S2

Let's say that Models of North America are represented by Na and N2

So we have to define the total ways of entries of E1 E2 S1 S2 N1 N2

We have to keep E1 E2 together and similarly N1 N2 together and similarly S1 S2 together so make three groups of two models from same region each

Arrangement of these three Group can be done in 3! ways

Arrangement of Models within Group can be done in 2!x2!x2! ways

i.e. Total Ways of Arranging the models so that they are grouped as per region together = (3!)*(2!x2!x2!) = 6*8 = 48

Answer: Option B
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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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New post 25 Jun 2015, 05:34
1
Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?

A. 72
B. 48
C. 64
D. 24
E. 8

Source: Platinum GMAT
Kudos for a correct solution.


Taking each of the 2 models from 3 continents as one unit , the 3 units can be arranged in 3! ways
Also, each of the pairs can be arranged in 2! ways
Therefore, total no of ways=3!*3*2!=48
Answer B
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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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New post 25 Jun 2015, 05:35
1
Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?

A. 72
B. 48
C. 64
D. 24
E. 8

Source: Platinum GMAT
Kudos for a correct solution.


Three groups can be arranged way= 3!..
within each group the two models can be arranged in 2! ways ..
total ways 3!*2!*2!*2!=48
ans B
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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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New post 25 Jun 2015, 05:37
KS15 wrote:
Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?

A. 72
B. 48
C. 64
D. 24
E. 8

Source: Platinum GMAT
Kudos for a correct solution.


Taking each of the 2 models from 3 continents as one unit , the 3 units can be arranged in 3! ways
Also, each of the pairs can be arranged in 2! ways
Therefore, total no of ways=3!*3*2!=48
Answer B



The highlighted part has calculation mistake 3!*3*2! = 36 :wink:

I hope it's just a typo error. :P
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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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New post 25 Jun 2015, 08:56
Out of 6 positions, 3 continents can be arranged in 3! Ways=6
Out of those 3 continents each 2 model can be arranged in 2!*2!*2! Ways= 8
So total number of arrangements for models to be arranged for 6 places =6*8=48

Hence answer is B

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There are six different models that are to appear in a fashion show.  [#permalink]

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New post 29 Jun 2015, 04:27
Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?

A. 72
B. 48
C. 64
D. 24
E. 8

Source: Platinum GMAT
Kudos for a correct solution.


Platinum GMAT Official Solution:

In this problem, order is important. Jane standing to the left of Mary is a different arrangement than Mary standing to the left of Jane. Because order is important, the permutations equation is used.

The formula for a permutation is:
nPr= n!/(n-r)!
where n is the total number of selections available and r is the number of items to be selected.

For each set of two models from each continent, there are 2P2ways to arrange them. From the permutation formula with n equal to 2 and r equal to 2 this results in:
2P2= 2! = 2

Since there three groups of two there are:
2P2*2P2*2P2 or 2*2*2 or 8 ways to arrange each group within each group.

Since there are three groups of models that can be placed in three different positions there are:
3P3ways to arrange the three groups.

The value of 3P3is (3*2*1)/(3-3)! = 6/0! = 6, or 6 ways to arrange the different groups. Note that 0! is defined to be equal to one.

Since there are 6 ways to arrange the groups and 8 ways to arrange the models within their own groups there are:
8X6 or 48 different ways to arrange the models.

So the correct answer is B.
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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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New post 08 Jul 2015, 03:45
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Hi Bunuel,

In your solution it says option A as the answer, must be a typo. Just to let you know.

Thanks.
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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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New post 08 Jul 2015, 05:52
2! X 2! X 2! X 3! = 48. (B)
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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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New post 08 Jul 2015, 22:25
Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?

A. 72
B. 48
C. 64
D. 24
E. 8

Source: Platinum GMAT
Kudos for a correct solution.


Since Models will sit in pair, So virtually we have 3 place and 3 Pairs to Sit. So three pair can take seat in 3*2 * 1 ways,
Each pair has 2 combination so (2*2*2) inter changeable combination within the pair.

So total combination = 3*2*1 * 2*2*2 = 48

Hence Option B should be correct.
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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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New post 05 Aug 2016, 15:48
3!*2!*2!*2! equals to 48

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Re: There are six different models that are to appear in a fashion show.  [#permalink]

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